A381551 Number of 2*n X 4 binary arrays with row sums 2 and column sums n, avoiding the patterns 010 and 101 in any row and column.

1, 4, 16, 64, 324, 1764, 10000, 58564, 350464, 2131600, 13133376, 81757764, 513294336, 3245580900, 20646241344, 132021769104, 848031024996, 5468890936356, 35392361925904, 229761144199876, 1495753923300484, 9762043084514704, 63858040015802256

Offset

0,2

Links

Christoph Koutschan, Table of n, a(n) for n = 0..1000

Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices, Enumerative Combinatorics and Applications 5:2, Article #S2R14, 2025.

Christoph Koutschan, Recurrence of order 10 with polynomial coefficients of degree 21.

Formula

a(n) ~ 4*phi^(4*n)/(Pi*sqrt(5)*n), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Feb 27 2025

Example

Here are 5 out of 16 solutions for n = 2:
  0 0 1 1   0 0 1 1   0 0 1 1   0 0 1 1   0 1 1 0
  0 0 1 1   0 1 1 0   1 0 0 1   1 1 0 0   1 0 0 1
  1 1 0 0   1 1 0 0   1 1 0 0   1 1 0 0   1 0 0 1
  1 1 0 0   1 0 0 1   0 1 1 0   0 0 1 1   0 1 1 0
the remaining ones are obtained from these by reflecting, rotating, or exchanging 0 and 1.

Crossrefs

Cf. A381553, A381554.

Sequence in context: A097679 A158778 A227313 * A155518 A005401 A002923

Adjacent sequences: A381548 A381549 A381550 * A381552 A381553 A381554

Keyword

nonn

Author

Christoph Koutschan, Feb 27 2025

Status

approved